complete the square to find the vertex of this parabola.

\x^2 - 16y - 4x - 12 = 0\

(?, )

Question

complete the square to find the vertex of this parabola.

\x^2 - 16y - 4x - 12 = 0\

(?,  )

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Completing the Square for Parabolas", "Parabola Properties" ], "current_concepts": [ "Completing the Square for Parabolas", "Parabola Properties" ] } ## Rearrange the equation to group x terms $$ x^2 - 4x = 16y + 12 $$ ## Complete the square for the x terms $$ \begin{aligned} x^2 - 4x + 4 &= 16y + 12 + 4 \ (x - 2)^2 &= 16y + 16 \ (x - 2)^2 &= 16(y + 1) \end{aligned} $$ ## Identify the vertex from the standard form $$ \begin{aligned} (x - h)^2 &= 4p(y - k) \ h = 2, &\quad k = -1 \ \text{Vertex} &= (2, -1) \end{aligned} $$ Complete the square to find the vertex of this parabola. $x^2 - 16y - 4x - 12 = 0$ (2, -1) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Completing the Square for Parabolas" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Rearrange the equation to group x terms

Complete the square for the x terms

Identify the vertex from the standard form

Answer: